Borrowing Constraint as an Optimal Contract
40 Pages Posted: 3 Jun 2010 Last revised: 6 Jun 2010
Date Written: October 20, 2009
Abstract
We study a continuous-time version of the optimal risk-sharing problem with one-sided commitment. In the optimal contract, the agent's consumption is non-decreasing and depends only on the maximal level of the agent's income realized to date. In the complete-markets implementation of the optimal contract, the Alvarez-Jermann solvency constraints take the form of a simple borrowing constraint familiar from the Bewley-Aiyagari incomplete-markets models. Unlike in the incomplete-markets models, however, the asset buffer stock held by the agent is negatively correlated with income.
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